brokerage bank accounts

You raise 3 issues: multiple bank accounts, accounts with different currencies, and fees.

Bank accounts are all separate. Even if you have two accounts with a single bank in one country, both linked to your broker via direct debit / direct credit arrangements, each account has its own balance and it’s own transaction history. You can use sweep arrangements and the like to automatically move funds from one account to another, but that’s not the same as depositing in one account and withdrawing those funds from another.

Banks always segregate currencies. Even if they say you have a single account with multiple currencies in it, they will report how much you hold of each currency separately. The closest that I’ve seen to being able to deposit and withdraw in different currencies in different countries are travel cards that allow you to load multiple currencies - if you run out of a currency, it can automatically draw from another currency within the account and do the conversion automatically. But even there, each currency is reported separately, and I’d expect that the FX conversions would appear in the transaction lists.

In relation to FX conversions, I have yet to see it done commercially without fees of some sort. Even if they call them bid-ask spreads or the like, the test is whether you can convert an amount from one currency to another and back again immediately, and expect to get back the original amount in the original currency. Since there are costs involved in facilitating FX conversions, it is normal business for the costs to be passed on to the consumer.